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Basic Kinetics Definition:
- the temporal & spatial distribution of a substance in a system
- measurement of Cp/time
- you know a graph is measuring the kinetics of a substance because time is on the X-axis & plasma concentration (Cp) is on the Y-axis
One Compartment Model
treats the body as one homogeneous volume in which mixing is INSTANTANEOUS; Input and output are from this one volume
Two Compartment Model
- when a drug distributes unevenly in the body, specifically it might move more quickly to a certain organ or part of the body than others
- this model involves 2 distinct distribution phases
- 1. initial distribution to specific areas of the body
- 2. followed by equilibration of the substance throughout the entire body
What are the two main compartments of a Two Compartment Model
- Compartment 1 (central): blood (plasma) & well perfused organs (eg. liver, kidney)
- Compartment 2 (peripheral): poorly perfused tissues (eg. muscle, lean tissue, fat)
First Pass Metabolism (Pre-systemic Extraction)
- a phenomenon of drug metabolism whereby the concentration of a drug is greatly reduced before it reaches the systemic circulation as a result of decreased absorption mediated by the liver &/or gut wall
- four primary systems that cause the first pass effect: enzymes of the GI lumen, gut wall enzymes, bacterial enzymes, & hepatic enzymes
- describes a drug administered any way except intravenously
- eg. orally, transdermally, sublingually, topically, etc.
When looking at a kinetics graph, how can you tell if a drug is administered extravascularly or intravenously?
- extravascularly: a LAG TIME will be seen between the drug being administered and it showing up in the plasma; something must happen before the drug is detected in blood
- intravenously: drug concentration should be detected immediately upon administration
- peak plasma concentration
- the point where rates of drug absorption, distribution, & clearance are at EQUILIBRIUM
- preceded by the absorptive phase and followed by the distribution phase
- the time when peak concentration is reached
- (X-axis value of Cmax data point)
- area under the plasma concentration curve
- systemic exposure to a drug
- the fraction of drug absorbed systemically after administration
- drugs administered intravenously have a bioavailability of 100%
- For drugs administered via other routes (extravascular), bioavailability is more commonly less than 100%
How is bioavailability calculated?
- fractional bioavailability of a drug
- to calculate F you must know the plasma concentration achieved when a drug is administered intravenously (CANNOT just use oral administration data)
- F = AUCoral / AUCIV
- the closer F is to 1, the greater the drug is absorbed systemically after administered extravascular
What is the main determinant of whether or not the FDA approves a GENERIC equivalent to a previously approved brand name drug?
- Bioavailability, or F value
- the generic version needs to exhibit a similar rate & extent of absorption as the original brand name drug
- AUC, Cmax and Tmax should all be statistically similar as well
What could cause a lower F value for a generic attempting to mimic the bioavailability of a name brand drug?
- 1. poor absorption (isn't lipophilic)
- 2. efflux transport (by P-glycoprotein)
- 3. pre-systemic extraction (either by hepatic enzymes or enteric CYP3A enzymes in GI mucosa)
Why is it important to monitor the blood level of some drugs, but not others?
- because some have a narrow therapeutic range - also is different for different people
- the #s that define therapeutic ranges are population averages & not specific for individuals
- 'every time a drug is given it's a mini experiment in the person it's given'
Why is the therapeutic range of antithrombotics (Heparin, Warfarin) measured differently from other drugs?
- because their serum concentration is useless, what matters is their effect on the body: whether or not they prevent blood clotting
- monitoring such drugs is pharmacodynamic, not pharmacokinetic
Volume of Distribution
- a number that gives us an idea of the POTENTIAL for a drug to distribute throughout the body
- tends to be a measure of lipophilicity*
- it's a proportionality constant that relates the amount of drug in the body to the concentration of drug in the plasma
- it's not a real number, but a hypothetical value used to describe potentials of drug distribution
Volume of Distribution Calculations for an IV Drug
- Vd = Dose [mass/concentration -> volume]
- aka the drug dose (D)
- plasma concentration (Cp)
- expressed in units of VOLUME (Liters)
- Vd: a GOOD MARKER OF DRUG LIPOPHILICITY
How would you calculate the Vd of a drug administered extravascularly instead of intravenously?
- bioavailability must be taken into account
- Vd = (Dose x F)
What does a low Vd (volume of distribution) indicate?
a low Vd indicates that a drug isn't in a central compartment (blood stream) but ELSEWHERE in the body
How many nanograms in 1 milligram?
- 109 ng = 1 mg
- 1012 ng = 1 kg
What does Vd (volume of distribution) FAIL to express?
- WHERE the drug is
- it just reflects peripheral tissue uptake
- refers to the situation where the overall intake of a drug is in dynamic equilibrium with its elimination
- is reached at a time that is 4-5 times a drug's half-life after regular dosing is started
Why is it useful to know the Vd of a drug?
- so the LOADING DOSE can be calculated
- this way a desired serum concentration can be achieved immediately (eg. for drugs - like antibiotics - that need to start working immediately)
Loading Dose Calculation
- DL = Vd * Cpdesired [vol * conc -> mass]
- dosage given when a drug is needed immediately because it allows therapeutic range to be reached almost right away in a patient
- loading doses are used frequently for antibiotics to combat serious bacterial infections
How is a desired plasma concentration maintained after the loading dose is given?
- by giving an additional maintenance dose
- the maintenance dose is given at a rate proportional to the elimination rate of the loading dose
- this way the amount of drug in the plasma remain constant because it's being replaced at the same rate at which it is being used up or lost (* assuming the drug exhibits first-order elimination behavior)
- Cl = dose rate = Q * E
- Cpsteady state
- units = volume/time, eg. mL/min (NO mass units)
- total volume of plasma from which drug is removed per unit time
- the quantitative capacity for the body to remove a drug
- determined by blood flow to the organ that functions to metabolize/clear the drug from the system (Q) & the efficiency of the organ in extracting the drug from the bloodstream (E)
Whole Body Clearance
- the volume of plasma cleared of its drug content per unit of time
- for drugs that exhibit first-order elimination, the RATE of elimination of a drug can vary as the concentration changes, but clearance will remain constant
What can be calculated if we know the clearance?
estimation of the time it takes to remove a drug from the body
What is clearance NOT?
- clearance is not the RATE of drug removal
- it's a component of it, but not the rate itself
blood flow to the organ that metabolizes or clears the drug
E (Extraction Ratio)
how effectively an organ extracts the drug from the bloodstream
Other Equations for Cl (clearance)
- Cl = dose/AUC
- Cl = Vd x k [from half life formula]
- Cl = Q x E
- Cl = elimination rate/Cp
- Cl = maintenance dose rate/Cp
How can the amount of drug eliminated from the plasma by that organ per unit time be calculated?
by knowing 1) the value for clearance by the organ responsible for removing the drug & 2) the plasma concentration of the drug in question
- the maximum possible clearance value
- is equal to blood flow to the clearing organ, as clearance can't exceed the amount of blood entering the organ
- eg. blood flow to the liver is 1500 mL/min
- maximal hepatic clearance (UL) of a drug susceptible to this route of elimination cannot exceed 1500 mL/min
When given 2 plots of drug concentration per unit time, how can one determine which plot for a given patient exhibits more efficient clearance?
- the plot with a LOWER AUC (area under the curve) indicates the drug is cleared more efficiently
- a high AUC value indicates low drug clearance and therefore high systemic exposure to said drug
- a slow clearance could be due to age, or compromised capacity of the organ system responsible for removing drug
What are the most common routes by which a drug is cleared from the body?
- 1. renal filtration (kidney)
- 2. metabolism: usually hepatic, but sometimes is done through the GI mucosa
- pathway of excretion usually elucidated during early studies
With the exception of what organ is specific organ clearance generally difficult to measure?
- filtration through the kidneys
- * but hepatic clearance is the most common route of drug clearance as it's the primary site of drug metabolism
Glomerular Filtration Rate (GFR)
- describes the flow rate of filtered fluid through the kidney
- important to take into consideration if a drug is excreted by renal filtration
- GFR = (140 – age) * IBW
- 72 x Scr
- for females multiply result by 0.85
- ideal body weight
- to calculate GFR using the Cockroft & Gault equation IBW is measured in kg
serum creatinine; measured to determine kidney function
Creatinine Clearance Rate (CCr or CrCl)
the volume of blood plasma that is cleared of creatinine per unit time (mL/min); is a useful measure for approximating the GFR
How is a drug dose adjusted if the CrCl is greater than 60?
100% of recommended dose is given every 6 hours
How is a drug dose adjusted if the CrCl is between 30-60?
50-75% of recommended dose is given every 8-12 hours
How is a drug dose adjusted if the CrCl is less than 30?
50% of recommended dose is given every 24 hours
- used as an indicator of liver function & a patient’s ability to metabolize drugs
- the HIGHER the score, the more likely the patient is to require a smaller drug dosage
- involves a constant amount of drug removal per unit time
- once the elimination mechanisms becomes saturated, elimination becomes zero-order
- rate of elimination is constant & independent of plasma concentration of drug
- drug clearance is dependent on drug concentration as a constant amount of drug is eliminated per unit of time
- this usually occurs when the elimination process is saturated
- few drugs used clinically exhibit zero-order behavior
What are two 'drugs' whose Km's are well below their therapeutic ranges?
- phenytoin (dilantin, an anticonvulsant)
- aka they exhibit zero-order elimination behavior
- such drugs possess non-linear kinetics, since plasma concentrations change more or less than expected upon changes in doses
- involves a constant fraction of drug removal per unit time
- when drug concentrations are low enough that the elimination mechanisms are not saturated, elimination is usually first-order
- rate of elimination depends and is directly proportional to plasma concentration of drug
- drug clearance however is independent of drug concentration (a constant fraction of drug is eliminated per unit of time)
- most drugs use exhibit first-order behavior at therapeutic concentrations
- such drugs possess linear kinetics since drug concentrations change in proportion to dose changes
Drug Elimination Behavior & Enzyme Kinetics
- *note: do not confuse behaviors during drug administration (above graph) with those during drug elimination
% drug cleared = fixed; amount = variable
- FIRST-ORDER BEHAVIOR
- Rate is proportional to Cp
- Clearance is independent of Cp
- Constant fraction eliminated per unit time
- Applicable to most drugs
- the Cp << Km
% drug cleared = variable; amount = fixed
- ZERO-ORDER BEHAVIOR
- Rate is constant & independent of Cp
- Clearance is dependent on Cp
- Constant amount eliminated per unit time
- Applicable to few drugs
- the Cp >> Km
- the time required for plasma CONCENTRATION of a drug to decrease by one half after absorption and distribution are complete [*only applies to drugs that follow first-order kinetics]
- when elimination follows first-order behavior the half-life of a drug is constant and independent of both dose administered & route of administration
Why is knowing the half-life of a drug useful?
- it is important for determining how long it takes to remove a given dose of a drug from the plasma
- it is important for determining the time to steady state concentration w/ continual administration of a drug (by either continuous infusion or multiple discreet doses)
For a drug that exhibits first-order kinetics, after how many half lives will more than 95% of it be eliminated from the body?
- after 5 half-lives have passed
- after 5 half lives such a drug would also be within 5% of the maximal steady state concentration
However the majority of drug is removed after about how many half lives have passed?
- he says 4 in lecture
- aka it would take ~40 hours to remove ~90% of a drug that has a half-life of 10 hours
How may half-life be graphically determined?
- from a semi-log scale of plasma concentration vs. time when the data is linear (aka after the drug has been absorbed)
- can determine half-life by simply looking at the plot and estimating the time it takes for the plasma concentration at any point during the decay to fall by 50%
- t1/2 = ln 2 ln 2 = 0.693
- k k = Cl / Vd
- t1/2 = 0.693 * Vd
- [most biologically accurate eqn]
- t1/2 = 0.693 / k k = ln (C1/C2)
- t1/2 = 0.693 * Δt ...
- ln (C1/C2)
What else can be calculated from a graph of plasma concentration vs. time?
- the volume of distribution IF we know the dose administered:
- Vd = Dose
- *always use initial plasma concentration (C0) from the graph when calculating Vd
Two Compartment Model
- appears as a biphasic plot (on a semi-log scale of plasma concentration vs time), not a linear one
- in the alpha (distribution phase) there is a rapid decrease in plasma concentration of the drug right administration, because it moves from the plasma to other tissue
- a linear decline of the drug concentration occurs after it has equilibrated between the various body compartments & the plasma
- this elimination phase is called the beta phase
How is Vd calculated for a drug that exhibits a two compartment model?
- to find the "initial plasma concentration" of the drug, you extrapolate back to the y-axis using the linear beta phase of the plot
- Vd = Dose
Half-life is a ______________ pharmacokinetic variable:
- half-life is a DEPENDENT pharmacokinetic variable
- its value depends on volume of distribution & clearance, each of which are independent of each other
t1/2 = 0.693 * Vd
- as volume distribution INCREASES, half-life increases (proportional)
- as Cl increases, half-life DECREASES (inversely proportional)
- the drug w/ the longest half-life should have the largest Vd (& vice versa)
In which case is the half-life shorter for a drug given orally or the same drug given parenterally?
- the half-lives are the SAME because it's the same drug & half-life is independent of ROUTE of administration
- (*absolute plasma concentrations will be different though)
- also, could use AUC's for PO (oral) & IV to get BIOAVAILABILITY
- F = AUCoral / AUCIV
Css (steady state concentration)
- Css = Dose / Vd
- plasma concentration of drug once a steady state has been achieved
- as a drug infusion progresses there reaches a point at which drug accumulation plateaus and then remains constant = steady state plasma concentration
- at steady state the rate of drug administration is equal to the rate of drug removal
After about how many half lives will a drug obeying first-order kinetics reach its steady state?
- ~4 half lives
- *TIME to reach the steady state is INDEPENDENT of the dose given (aka giving a lot won't help you reach the drug's steady state any faster, it's dependent on body's ability to metabolize - however if a larger dose is given the plasma concentration will be higher)
How can dose adjustments be made for a drug that obeys first-order kinetics?
- Dnew= Dold*(Cssdesired / Cssobserved)
- by basing the adjustments on plasma concentrations
- plasma concentrations of first-order drugs change IN PROPORTION to dose
The drug concentration reached at steady state is a function of dose administered divided by what?
dose administered / the volume of distribution for that drug
If a drug's steady state concentration is 4 concentration units (mg/mL), what would need to be done to raise its steady state concentration to 8 mg/mL? Lower it to 2 mg/mL?
- 8: the infusion rate (Q) would need to be DOUBLED
- 2: the infusion rate (Q) would need to be HALVED
- (eg. if Q4 = 10 mg/min, to reach an ss conc. of 8, Q --> 20 mg/min)
Equation used to calculate plasma concentrations of drugs that exhibit first-order behavior in a one-compartment model:
- C = C0e-kt
- C0 = initial concentration
- k = elimination rate constant
- t = time since drug was 1st given
What are the implications of C = C0e-kt?
- if you can determine the concentration of a drug in the plasma at any given time and you know k, it is possible to determine what the drug concentration will be at any subsequent time
- it's also possible to determine at what point in time the concentration would fall below some minimum effective level (i.e. when you might given another dose of the drug)
describes the maximum plasma concentration of a drug over a dosing interval
describes the minimum concentration over the dosing interval
- the ratio of the Cmax to the Cmin
- it's dependent on the drug dose & the frequency with which it's given
If a drug exhibits first-order clearance, what happens if both dose and frequency change in equal proportions?
- the interdose fluctuation should change but the mean steady state plasma concentration should NOT as long as the total dose administered per day remains the same
- eg. if an antibiotic is given orally, 125 mg every 6 hours, mean steady state plasma concentration = 15 mcg/mL
- if the dose & interval were changed to 250 mg every 12 hours or 500 mg every 24 hours, the interdose fluctuation would INCREASE, but the mean steady state concentration would stay the same
What is the only way to obtain perfectly constant plasma levels of a drug?
- a continuous infusion
- for other routes of administration the degree of fluctuation of plasma drug concentrations can be altered by changing the dose interval while holding the dose rate constant
- shorter dose intervals result in less fluctuation than longer dose intervals
- the generic name for a group of enzymes responsible for most drug metabolism oxidation reactions
- eg. CYP450 1A2, 2C19, 2D6, 3A4
- they're present mainly in the liver, although CYP450 3A is also present in the GI mucosa
What are some strong inhibitors of the CYP450 system?
- ritonavir (Norvir): HIV protese inhibitor
- macrolide antibiotics (erythromycin aka Zpak)
- azole antifungals
- grapefruit juice*
What are some strong inducers of the CYP450 system?
- rifampin (antibiotic)
- anticonvulsants (carbamazepine/Tegretal, phenytoin/Dilantin, phenobarbital)
Example of a drug-drug interaction:
- Ciprofloxacin & Vitamins
- because the drugs were being taken at the same time, an interaction occurred due to the fact that cipro can form cations with the minerals in vitamins
- this complex results it neither drug being absorbed very well in the GI tract
- *can be avoided by staggering administration times (ideally by at least 4 hours)
What is an example of a drug that requires an acidic environment for optimal absorption?
- azole antifungals
- anything that raises the pH of the stomach or arbitrary environment where such a drug is absorbed affects effectiveness of the medication (because less of it is internalized)
- eg. prilosec suppresses acid production --> less of anti-fungal is absorbed --> treatment failure
- difficult to avoid if both drugs are required
Why would you perform therapeutic drug monitoring?
- Drug has a narrow therapeutic window
- There's a relationship between Cp & either efficacy or toxicity
- Drug has a unpredictable dose-response relationship
- Reliable assay exists
- often done for Antiarrhythmics (digoxin, procainamide), Antibiotics (aminoglycosides), Anticonvulsants (carbamazepine, phenytoin), Antidepressants (amitriptyline, imipramine) & Antithrombotics (heparin, warfarin)
- antibiotics (eg. gentamicin, tobramycin) that are VERY polar/hydrophobic - lends itself to therapeutic drug monitoring
- they cannot be given orally, must be given parenterally using a dosage based on a patient's ideal body weight (unless obese, in which case a dosing weight must be calculated)
- DW = IBW + 0.4(TBW - IBW)
- the rate limiting step of aminoglycosides' half-life = KIDNEY FUNCTION
- there is no hepatic or 1st pass metabolism; the drug is cleared through the kidney in it's original form
- Vd = 0.3-0.5 L/kg
- therefore the half-life depends on kidney function but usually is around 2-4 hours if healthy (need to be careful)